Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 9137)

Label	Polynomial	Discriminant	Galois group	Class group
9.9.9685993193.1	x^9 - 9x^7 + 24x^5 - 2x^4 - 20x^3 + 3x^2 + 5x - 1	\( 9685993193 \)	$S_9$ (as 9T34)	Trivial
9.9.11779563529.1	x^9 - 9x^7 - 2x^6 + 22x^5 + 5x^4 - 17x^3 - 4x^2 + 4x + 1	\( 11779563529 \)	$S_9$ (as 9T34)	Trivial
9.9.16240385609.1	x^9 - x^8 - 9x^7 + 4x^6 + 26x^5 - 2x^4 - 25x^3 - x^2 + 7x + 1	\( 7^{6}\cdot 138041 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.16440305941.1	x^9 - 2x^8 - 9x^7 + 11x^6 + 28x^5 - 18x^4 - 34x^3 + 8x^2 + 13x + 1	\( 37^{2}\cdot 229^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.9.16898785417.1	x^9 - 2x^8 - 7x^7 + 11x^6 + 18x^5 - 17x^4 - 19x^3 + 6x^2 + 7x + 1	\( 17\cdot 994046201 \)	$S_9$ (as 9T34)	Trivial
9.9.16983563041.1	x^9 - x^8 - 8x^7 + 7x^6 + 21x^5 - 15x^4 - 20x^3 + 10x^2 + 5x - 1	\( 19^{8} \)	$C_9$ (as 9T1)	Trivial
9.9.17515230173.1	x^9 - 4x^8 - 3x^7 + 29x^6 - 26x^5 - 24x^4 + 34x^3 - 2x^2 - 5x + 1	\( 7^{6}\cdot 53^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.18625670317.1	x^9 - 9x^7 - x^6 + 23x^5 + 4x^4 - 19x^3 - 3x^2 + 4x + 1	\( 18625670317 \)	$S_9$ (as 9T34)	Trivial
9.9.18756753353.1	x^9 - 3x^8 - 4x^7 + 15x^6 + 4x^5 - 22x^4 - x^3 + 10x^2 - 1	\( 13\cdot 11743\cdot 122867 \)	$S_9$ (as 9T34)	Trivial
9.9.19936446593.1	x^9 - 3x^8 - 5x^7 + 17x^6 + 7x^5 - 30x^4 - x^3 + 16x^2 - 2x - 1	\( 7^{6}\cdot 169457 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.20370652633.1	x^9 - x^8 - 8x^7 + 8x^6 + 17x^5 - 15x^4 - 12x^3 + 8x^2 + 2x - 1	\( 20370652633 \)	$S_9$ (as 9T34)	Trivial
9.9.22211510281.1	x^9 - x^8 - 9x^7 + 3x^6 + 22x^5 - x^4 - 17x^3 - 2x^2 + 4x + 1	\( 22211510281 \)	$S_9$ (as 9T34)	Trivial
9.9.22384826361.1	x^9 - 9x^7 - x^6 + 24x^5 + 3x^4 - 22x^3 + 6x - 1	\( 3^{12}\cdot 73\cdot 577 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.23041013113.1	x^9 - 9x^7 - x^6 + 24x^5 + 3x^4 - 21x^3 - 4x^2 + 5x + 1	\( 23041013113 \)	$S_9$ (as 9T34)	Trivial
9.9.25405254289.1	x^9 - x^8 - 9x^7 + 5x^6 + 22x^5 - 8x^4 - 17x^3 + 5x^2 + 4x - 1	\( 25405254289 \)	$S_9$ (as 9T34)	Trivial
9.9.29297320489.1	x^9 - 3x^8 - 5x^7 + 19x^6 + 4x^5 - 36x^4 + 9x^3 + 18x^2 - 9x + 1	\( 23\cdot 1273796543 \)	$S_9$ (as 9T34)	Trivial
9.9.29397823793.1	x^9 - x^8 - 9x^7 + 5x^6 + 22x^5 - 8x^4 - 16x^3 + 5x^2 + 3x - 1	\( 13\cdot 373\cdot 1229\cdot 4933 \)	$S_9$ (as 9T34)	Trivial
9.9.29430250297.1	x^9 - x^8 - 8x^7 + 6x^6 + 20x^5 - 11x^4 - 18x^3 + 7x^2 + 4x - 1	\( 7^{6}\cdot 250153 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.30609108809.1	x^9 - 2x^8 - 7x^7 + 12x^6 + 17x^5 - 20x^4 - 18x^3 + 8x^2 + 7x + 1	\( 61\cdot 5171\cdot 97039 \)	$S_9$ (as 9T34)	Trivial
9.9.31381059609.1	x^9 - 9x^7 + 27x^5 - 30x^3 + 9x - 1	\( 3^{22} \)	$C_9$ (as 9T1)	Trivial
9.9.32202550729.1	x^9 - x^8 - 9x^7 + 5x^6 + 26x^5 - 5x^4 - 24x^3 + x^2 + 6x + 1	\( 19\cdot 31\cdot 54673261 \)	$S_9$ (as 9T34)	Trivial
9.9.33600968473.1	x^9 - x^8 - 9x^7 + 11x^6 + 20x^5 - 27x^4 - 10x^3 + 17x^2 - 2x - 1	\( 33600968473 \)	$S_9$ (as 9T34)	Trivial
9.9.34189107913.1	x^9 - x^8 - 8x^7 + 8x^6 + 18x^5 - 17x^4 - 12x^3 + 10x^2 + x - 1	\( 1019\cdot 33551627 \)	$S_9$ (as 9T34)	Trivial
9.9.34651324493.1	x^9 - 4x^8 - 2x^7 + 22x^6 - 10x^5 - 34x^4 + 25x^3 + 10x^2 - 8x + 1	\( 34651324493 \)	$S_9$ (as 9T34)	Trivial
9.9.34800272761.1	x^9 - 3x^8 - 5x^7 + 17x^6 + 9x^5 - 30x^4 - 8x^3 + 16x^2 + 3x - 1	\( 34800272761 \)	$S_9$ (as 9T34)	Trivial
9.9.35754308089.1	x^9 - 2x^8 - 7x^7 + 11x^6 + 14x^5 - 17x^4 - 10x^3 + 8x^2 + 2x - 1	\( 7283\cdot 4909283 \)	$S_9$ (as 9T34)	Trivial
9.9.35896709933.1	x^9 - 2x^8 - 7x^7 + 11x^6 + 16x^5 - 19x^4 - 13x^3 + 11x^2 + 2x - 1	\( 7^{6}\cdot 463\cdot 659 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.36288414161.1	x^9 - 2x^8 - 7x^7 + 15x^6 + 11x^5 - 29x^4 + 13x^2 - 2x - 1	\( 409\cdot 88724729 \)	$S_9$ (as 9T34)	Trivial
9.9.36446755221.1	x^9 - 9x^7 - x^6 + 24x^5 + 6x^4 - 18x^3 - 6x^2 + 3x + 1	\( 3^{12}\cdot 68581 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.36763077169.1	x^9 - 4x^8 - 2x^7 + 22x^6 - 14x^5 - 22x^4 + 20x^3 + 2x^2 - 5x + 1	\( 7^{6}\cdot 13^{2}\cdot 43^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.36911831833.1	x^9 - 2x^8 - 7x^7 + 11x^6 + 17x^5 - 17x^4 - 15x^3 + 8x^2 + 4x - 1	\( 139\cdot 265552747 \)	$S_9$ (as 9T34)	Trivial
9.9.37161412073.1	x^9 - x^8 - 8x^7 + 6x^6 + 19x^5 - 11x^4 - 15x^3 + 6x^2 + 3x - 1	\( 101\cdot 367934773 \)	$S_9$ (as 9T34)	Trivial
9.9.53038958912.1	x^9 - x^8 - 9x^7 + 6x^6 + 22x^5 - 9x^4 - 17x^3 + 5x^2 + 4x - 1	\( 2^{6}\cdot 37^{3}\cdot 16361 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.9.53286643921.1	x^9 - 2x^8 - 8x^7 + 18x^6 + 10x^5 - 36x^4 + 10x^3 + 12x^2 - 7x + 1	\( 7^{6}\cdot 673^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.62523502209.1	x^9 - 15x^7 - 4x^6 + 54x^5 + 12x^4 - 38x^3 - 9x^2 + 6x + 1	\( 3^{12}\cdot 7^{6} \)	$C_3^2$ (as 9T2)	Trivial
9.9.63162460553.1	x^9 - x^8 - 11x^7 + 9x^6 + 34x^5 - 10x^4 - 39x^3 - 12x^2 + 3x + 1	\( 61^{2}\cdot 257^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.9.69573030289.1	x^9 - x^8 - 10x^7 + 14x^6 + 20x^5 - 36x^4 + 18x^2 - 8x + 1	\( 7^{6}\cdot 769^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.69775386569.1	x^9 - 10x^7 - 2x^6 + 31x^5 + 11x^4 - 30x^3 - 16x^2 + x + 1	\( 7^{6}\cdot 593081 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.74724856128.1	x^9 - 3x^8 - 9x^7 + 14x^6 + 24x^5 - 15x^4 - 21x^3 + 3x^2 + 6x + 1	\( 2^{6}\cdot 3^{12}\cdot 13^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.80174499328.1	x^9 - 4x^8 - 6x^7 + 29x^6 + 19x^5 - 63x^4 - 41x^3 + 18x^2 + 5x - 1	\( 2^{9}\cdot 7^{6}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.100602531136.1	x^9 - 3x^8 - 5x^7 + 20x^6 - 31x^4 + 7x^3 + 15x^2 - 2x - 1	\( 2^{6}\cdot 37^{3}\cdot 31033 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.9.114864601117.1	x^9 - 4x^8 - 4x^7 + 24x^6 + 4x^5 - 40x^4 - x^3 + 20x^2 - 1	\( 7^{6}\cdot 41\cdot 23813 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.9.139858796529.1	x^9 - 18x^7 - 3x^6 + 45x^5 + 9x^4 - 36x^3 - 9x^2 + 9x + 3	\( 3^{18}\cdot 19^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.144872805473.1	x^9 - 4x^8 - 4x^7 + 28x^6 - 14x^5 - 29x^4 + 15x^3 + 10x^2 - 3x - 1	\( 11^{3}\cdot 37^{2}\cdot 43^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.9.164648481361.1	x^9 - 14x^7 + 63x^5 - 98x^3 + 42x - 7	\( 7^{8}\cdot 13^{4} \)	$C_9:C_3$ (as 9T6)	Trivial
9.9.174583151469.1	x^9 - 12x^7 - 3x^6 + 36x^5 + 6x^4 - 30x^3 + 6x - 1	\( 3^{15}\cdot 23^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.177559431424.1	x^9 - 4x^8 - 4x^7 + 22x^6 + 10x^5 - 36x^4 - 18x^3 + 16x^2 + 12x + 2	\( 2^{8}\cdot 37^{3}\cdot 13693 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.9.183637853504.1	x^9 - 14x^7 - 8x^6 + 56x^5 + 56x^4 - 44x^3 - 56x^2 + 8	\( 2^{6}\cdot 7^{6}\cdot 29^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.187076145529.1	x^9 - 15x^7 - 10x^6 + 47x^5 + 23x^4 - 52x^3 - 5x^2 + 13x - 1	\( 7^{6}\cdot 13^{2}\cdot 97^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial
9.9.188860645561.1	x^9 - x^8 - 12x^7 + 42x^5 + 28x^4 - 28x^3 - 32x^2 - 10x - 1	\( 7^{8}\cdot 181^{2} \)	$C_3 \wr C_3 $ (as 9T17)	Trivial